SOLUTION: Show that (b+a)sinA = acos½(B+C), where A, B and C are angles of a triangle and a, b and c are corresponding sides.

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Question 1131928: Show that (b+a)sinA = acos½(B+C), where A, B and C are angles of a triangle and a, b and c are corresponding sides.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28b%2Ba%29sin%28A%29+=+a%2Acos%28expr%281%2F2%29%28B%2BC%29%29
This is not true in general because if it were true in general it
would hold true for an equilateral triangle with

a = b = c = 1 and A = B = C = 60°

Substituting:

 

%282%29%28sqrt%283%29%2F2%29+=+1%2Acos%28expr%281%2F2%29%28%22120%B0%22%29%29

%282%29%28sqrt%283%29%2F2%29+=+1%2Acos%28%2260%B0%22%29 

%28cross%282%29%29%28sqrt%283%29%2Fcross%282%29%29+=+1%2A%281%2F2%29

sqrt%283%29+=+1%2F2

Which is false.  So since it is false for an equilateral triangle
with all sides 1 and all angles 60°, it is NOT true in general.
If you inadvertently typed it incorrectly, you may tell me in the
form below and I'll get back to you by email. There is never any
charge as I am a retired mathematics teacher and I do this for fun.

Edwin